English

Solving $\overline\partial$ with prescribed support on Hartogs triangles in $\mathbb C^2$ and $\mathbb C\mathbb P^2$

Complex Variables 2016-09-15 v1

Abstract

In this paper we study the solvability of the Cauchy-Riemann equation with prescibed support in different spaces of forms. The unbounded Hartogs triangle in C2\mathbb C^2 and the Hartogs domains in CP2\mathbb C\mathbb P^2 provide us new unexpected phenomena. In particular we prove that the Dolbeault isomorphism fails to hold for the Dolbeault cohomology with prescribed support

Keywords

Cite

@article{arxiv.1609.04194,
  title  = {Solving $\overline\partial$ with prescribed support on Hartogs triangles in $\mathbb C^2$ and $\mathbb C\mathbb P^2$},
  author = {Christine Laurent-Thiébaut and Mei-Chi Shaw},
  journal= {arXiv preprint arXiv:1609.04194},
  year   = {2016}
}
R2 v1 2026-06-22T15:49:24.479Z